Question: Simplify. Remove all perfect squares from inside the square root. Assume $b$ is positive. $\sqrt{48b^7}=$
Answer: Factor $48$ and find the greatest perfect square: $48=2\cdot 2\cdot 2\cdot 2\cdot 3=4^2\cdot 3$ Find the greatest perfect square in $b^7$ : $b^7=\left(b^3\right)^2\cdot b$ $\begin{aligned} \sqrt{48b^7}&=\sqrt{4^2\cdot 3\cdot \left(b^3\right)^2\cdot b} \\\\ &=\sqrt{4^2}\cdot \sqrt{3} \cdot \sqrt{\left(b^3\right)^2}\cdot \sqrt{b} \\\\ &=4\cdot \sqrt{3} \cdot b^3\cdot \sqrt{b} \\\\ &=4b^3\sqrt{3b} \end{aligned}$